Thermodynamics, 5th Edition

(1.5.12b)

ordinarily depends on path taken, i.e., on the manner in which the force varies with displacement, when x is changed from x₁ to x₂. For obvious reasons, it is difficult to develop a sensible theory if, for a specific difference in end points, the integrals (changes in properties) depend on the chosen path. One is thus led to the important task of seeking out integrals that depend solely on the end points—quantities that were described in Section 1.3 as functions of state. Such integrals also vanish identically when x₁=x₂.

For this purpose, consider a process for which we select a particular coordinate x₁=0 that is arbitrary but, once ...